Problem: Simplify the following expression: $ y = \dfrac{p - 6}{8} - \dfrac{7}{6} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{p - 6}{8} \times \dfrac{6}{6} = \dfrac{6p - 36}{48} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{7}{6} \times \dfrac{8}{8} = \dfrac{56}{48} $ Therefore $ y = \dfrac{6p - 36}{48} - \dfrac{56}{48} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{6p - 36 - 56 }{48} $ Distribute the negative sign: $y = \dfrac{6p - 36 - 56}{48}$ $y = \dfrac{6p - 92}{48}$ Simplify the expression by dividing the numerator and denominator by 2: $y = \dfrac{3p - 46}{24}$